Two particles are in a uniform electric field whose value is +4000 N/C. The mass and charge of particle 1 are m1 = 1.0x10-5 kg and q1 = -15 µC, while the corresponding values for particle 2 are m2 = 3.0 x10-5 kg and q2 = +35.0 µC. Initially the particles are at rest. The particles are both located on the same electric field line but are separated from each other by a distance d. When released, they accelerate but always remain at this same distance from each other. Find the separation distance.

I used the E1=E2 but i'm stuck on the algebra.

To find the separation distance between the two particles, we can start by equating the electric forces acting on the two particles.

The electric force (F) experienced by a charged particle in an electric field is given by the equation F = q * E, where q is the charge of the particle and E is the electric field strength.

For particle 1, the electric force is F1 = q1 * E. Similarly, for particle 2, the electric force is F2 = q2 * E.

Since both particles experience the same electric field, we can set F1 equal to F2, giving us:

q1 * E = q2 * E

Now, let's substitute the given values for the charges and electric field:

(-15 µC) * (4000 N/C) = (35 µC) * (4000 N/C)

To make the calculations easier, we can convert the charges to coulombs:

(-15 µC) * (1x10^-6 C/µC) = (35 µC) * (1x10^-6 C/µC)

Next, we can simplify the equation:

-15x10^-6 C = 35x10^-6 C

We can now solve for the separation distance (d). The electric force between the two particles is attractive due to the opposite signs of their charges. The electric force is given by Coulomb's Law:

F = k * (|(q1 * q2)| / d^2)

Where k is Coulomb's constant (k = 9x10^9 Nm^2/C^2).

We know that the magnitude of the electric force is the same for both particles, so we can set up the following equation:

k * (|(q1 * q2)| / d^2) = k * (|(q1 * q2)| / d^2)

Substituting the given values:

(9x10^9 Nm^2/C^2) * (|-15x10^-6 C * 35x10^-6 C| / d^2) = (9x10^9 Nm^2/C^2) * (|-15x10^-6 C * 35x10^-6 C| / d^2)

Now, let's simplify the equation further:

|-15x10^-6 C * 35x10^-6 C| = |-15x35| * (10^-6 C)^2

|-15x10^-6 C * 35x10^-6 C| = |-525| * (10^-6 C)^2

|-15x10^-6 C * 35x10^-6 C| = 525 * (10^-12 C^2)

|-15x10^-6 C * 35x10^-6 C| = 525x10^-12 C^2

Finally, we can solve for the separation distance (d) by rearranging the equation:

d^2 = (525x10^-12 C^2) / (9x10^9 Nm^2/C^2)

d^2 = (525/9) x (10^-12/10^-9) * (C^2 / Nm^2)

d^2 = (525/9) x (10^-12/10^-9) * (C^2 / Nm^2)

d^2 = (525/9) x (10^-3) * (C^2 / Nm^2)

d^2 = (525/9) x 10^-3 m^2

Let's perform the calculation to find d:

d^2 = (525/9) x 10^-3

d^2 = 58.333 x 10^-3

d^2 = 0.058333

Taking the square root of both sides, we get:

d ≈ 0.241 meters

Therefore, the separation distance between the two particles is approximately 0.241 meters.